class: center, middle, inverse, title-slide # Controls ## Telling endogeneity we’ve had ENOUGH ### Updated 2020-08-08 --- # Endogeneity - Last week was all about handling sampling variation and avoiding inference error - This week we're all about endogeneity! - Where it pops up and what we can do about it - At least as a starter (we'll revisit this topic many times) --- # Endogeneity Recap - We believe that our true model looks like this: `$$Y = \beta_0 + \beta_1X+\varepsilon$$` - Where `\(\varepsilon\)` is *everything that determines `\(Y\)` other than `\(X\)`* - If `\(X\)` is related to some of those things, we have endogeneity - Estimating the above model by OLS, it will mistake the effect of those *other* things for the effect of `\(X\)`, and our estimate of `\(\hat{\beta}_1\)` won't represent the true `\(\beta_1\)` no matter how many observations we have --- # Endogeneity Recap - For example, the model `$$IceCreamEating = \beta_0 + \beta_1ShortsWearing + \varepsilon$$` - The true `\(\beta_1\)` is probably `\(0\)`. But since `\(Temperature\)` is in `\(\varepsilon\)` and `\(Temperature\)` is related to `\(ShortsWearing\)`, OLS will mistakenly assign the effect of `\(Temperature\)` to the effect of `\(ShortsWearing\)`, making it look like there's a positive effect when there isn't one - Here we're mistakenly finding a positive effect when the truth is `\(0\)`, but it could be anything - negative effect when truth is `\(0\)`, positive effect when the truth is a bigger/smaller positive effect, negative effect when truth is positive, etc. etc. --- # To the Rescue - One way we can solve this problem is through the use of *control variables* - What if `\(Temperature\)` *weren't* in `\(\varepsilon\)`? Then we'd be fine! How do we take it out? Just put it in the model directly! `$$IceCreamEating = \beta_0 + \beta_1ShortsWearing + \beta_2Temperature + \varepsilon$$` - Now we have a *multivariate* regression model. Our estimate `\(\hat{\beta}_1\)` will *not* be biased by `\(Temperature\)` because we've controlled for it <span style = "font-size: small">(probably more accurate to say "covariates" or "variables to adjust for" than "control variables" and "adjust for" rather than "control for" but hey what are you gonna do, "control" is standard)</span> --- # To the Rescue - So the task of solving our endogeneity problems in estimating `\(\beta_1\)` using `\(\hat{\beta}_1\)` comes down to us *finding all the elements of `\(\varepsilon\)` that are related to `\(X\)` and adding them to the model* - As we add them, they leave `\(\varepsilon\)` and hopefully we end up with a version of `\(\varepsilon\)` that is no longer related to `\(X\)` - If `\(cov(X,\varepsilon) = 0\)` then we have an unbiased estimate! - (of course, we have no way of checking if that's true - it's based on what we think the data generating process looks like) --- # How? - How does this actually work? - Controlling for a variable works by *removing variation in `\(X\)` and `\(Y\)` that is explained by the control variable* - So our estimate of `\(\hat{\beta}_1\)` is based on *just the variation in `\(X\)` and `\(Y\)` that is unrelated to the control variable - Any accidentally-assigning-the-value-of-Temperature-to-ShortsWearing can't happen because we've removed the effect of `\(Temperature\)` on `\(ShortsWearing\)` as well as the effect of `\(Temperature\)` on `\(IceCreamEating\)` - We're asking at that point, *holding `\(Temperature\)` constant*, i.e. *comparing two different days with the same `\(Temperature\)` *, how is `\(ShortsWearing\)` related to `\(IceCreamEating\)`? - We know we're comparing within the same `\(Temperature\)` because we literally subtracted out all the `\(Temperature\)` differences! --- # Example The true effect is `\(\beta_1 = 3\)`. Notice `\(Z\)` is binary and is related to `\(X\)` and `\(Y\)` but isn't in the model! ```r tib <- tibble(Z = 1*(rnorm(1000) > 0)) %>% mutate(X = Z + rnorm(1000)) %>% mutate(Y = 2 + 3*X + 2*Z + rnorm(1000)) tib %>% lm(Y~X, data = .) %>% export_summs(statistics = c(N = 'nobs')) ``` <table class="huxtable" style="border-collapse: collapse; border: 0px; margin-bottom: 2em; margin-top: 2em; ; margin-left: auto; margin-right: auto; " id="tab:unnamed-chunk-2"> <col><col><tr> <th style="vertical-align: top; text-align: center; white-space: normal; border-style: solid solid solid solid; border-width: 0.8pt 0pt 0pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;"></th><th style="vertical-align: top; text-align: center; white-space: normal; border-style: solid solid solid solid; border-width: 0.8pt 0pt 0.4pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">Model 1</th></tr> <tr> <th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">(Intercept)</th><td style="vertical-align: top; text-align: right; white-space: normal; border-style: solid solid solid solid; border-width: 0.4pt 0pt 0pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">2.76 ***</td></tr> <tr> <th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;"></th><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">(0.05)   </td></tr> <tr> <th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">X</th><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">3.42 ***</td></tr> <tr> <th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;"></th><td style="vertical-align: top; text-align: right; white-space: normal; border-style: solid solid solid solid; border-width: 0pt 0pt 0.4pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">(0.04)   </td></tr> <tr> <th style="vertical-align: top; text-align: left; white-space: normal; border-style: solid solid solid solid; border-width: 0pt 0pt 0.8pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">N</th><td style="vertical-align: top; text-align: right; white-space: normal; border-style: solid solid solid solid; border-width: 0.4pt 0pt 0.8pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">1000       </td></tr> <tr> <th colspan="2" style="vertical-align: top; text-align: left; white-space: normal; border-style: solid solid solid solid; border-width: 0.8pt 0pt 0pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;"> *** p < 0.001; ** p < 0.01; * p < 0.05.</th></tr> </table> --- # Example To remove what part of `\(X\)` and `\(Y\)` is explained by `\(Z\)`, we can get the mean of `\(X\)` and `\(Y\)` by values of `\(Z\)` ```r tib <- tib %>% group_by(Z) %>% mutate(Y_mean = mean(Y), X_mean = mean(X)) head(tib) ``` ``` ## # A tibble: 6 x 5 ## # Groups: Z [2] ## Z X Y Y_mean X_mean ## <dbl> <dbl> <dbl> <dbl> <dbl> ## 1 1 0.855 5.98 6.91 0.967 ## 2 1 -1.59 -0.226 6.91 0.967 ## 3 1 0.806 6.08 6.91 0.967 ## 4 1 -0.0302 2.94 6.91 0.967 ## 5 0 -0.490 -0.997 1.95 -0.0121 ## 6 0 -0.512 0.383 1.95 -0.0121 ``` --- # Example Now, `Y_mean` and `X_mean` are the mean of `Y` and `X` for the values of `Z`, i.e. the part of `Y` and `X` *explained by `Z`*. So subtract those parts out to get *residuals* `Y_res` and `X_res`! ```r tib <- tib %>% mutate(Y_res = Y - Y_mean, X_res = X - X_mean) head(tib) ``` ``` ## # A tibble: 6 x 7 ## # Groups: Z [2] ## Z X Y Y_mean X_mean Y_res X_res ## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> ## 1 1 0.855 5.98 6.91 0.967 -0.928 -0.113 ## 2 1 -1.59 -0.226 6.91 0.967 -7.14 -2.55 ## 3 1 0.806 6.08 6.91 0.967 -0.827 -0.161 ## 4 1 -0.0302 2.94 6.91 0.967 -3.98 -0.997 ## 5 0 -0.490 -0.997 1.95 -0.0121 -2.95 -0.478 ## 6 0 -0.512 0.383 1.95 -0.0121 -1.57 -0.499 ``` --- # Example What do we get now? ```r tib %>% lm(Y_res ~ X_res, data = .) %>% export_summs(statistics = c(N = 'nobs')) ``` <table class="huxtable" style="border-collapse: collapse; border: 0px; margin-bottom: 2em; margin-top: 2em; ; margin-left: auto; margin-right: auto; " id="tab:unnamed-chunk-5"> <col><col><tr> <th style="vertical-align: top; text-align: center; white-space: normal; border-style: solid solid solid solid; border-width: 0.8pt 0pt 0pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;"></th><th style="vertical-align: top; text-align: center; white-space: normal; border-style: solid solid solid solid; border-width: 0.8pt 0pt 0.4pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">Model 1</th></tr> <tr> <th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">(Intercept)</th><td style="vertical-align: top; text-align: right; white-space: normal; border-style: solid solid solid solid; border-width: 0.4pt 0pt 0pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">0.00    </td></tr> <tr> <th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;"></th><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">(0.03)   </td></tr> <tr> <th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">X_res</th><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">3.03 ***</td></tr> <tr> <th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;"></th><td style="vertical-align: top; text-align: right; white-space: normal; border-style: solid solid solid solid; border-width: 0pt 0pt 0.4pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">(0.03)   </td></tr> <tr> <th style="vertical-align: top; text-align: left; white-space: normal; border-style: solid solid solid solid; border-width: 0pt 0pt 0.8pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">N</th><td style="vertical-align: top; text-align: right; white-space: normal; border-style: solid solid solid solid; border-width: 0.4pt 0pt 0.8pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">1000       </td></tr> <tr> <th colspan="2" style="vertical-align: top; text-align: left; white-space: normal; border-style: solid solid solid solid; border-width: 0.8pt 0pt 0pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;"> *** p < 0.001; ** p < 0.01; * p < 0.05.</th></tr> </table> --- # Example Compare this to actually including `Z` as a control: ```r tib %>% lm(Y ~ X + Z, data = .) %>% export_summs(statistics = c(N = 'nobs')) ``` <table class="huxtable" style="border-collapse: collapse; border: 0px; margin-bottom: 2em; margin-top: 2em; ; margin-left: auto; margin-right: auto; " id="tab:unnamed-chunk-6"> <col><col><tr> <th style="vertical-align: top; text-align: center; white-space: normal; border-style: solid solid solid solid; border-width: 0.8pt 0pt 0pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;"></th><th style="vertical-align: top; text-align: center; white-space: normal; border-style: solid solid solid solid; border-width: 0.8pt 0pt 0.4pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">Model 1</th></tr> <tr> <th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">(Intercept)</th><td style="vertical-align: top; text-align: right; white-space: normal; border-style: solid solid solid solid; border-width: 0.4pt 0pt 0pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">1.99 ***</td></tr> <tr> <th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;"></th><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">(0.04)   </td></tr> <tr> <th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">X</th><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">3.03 ***</td></tr> <tr> <th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;"></th><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">(0.03)   </td></tr> <tr> <th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">Z</th><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">1.99 ***</td></tr> <tr> <th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;"></th><td style="vertical-align: top; text-align: right; white-space: normal; border-style: solid solid solid solid; border-width: 0pt 0pt 0.4pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">(0.07)   </td></tr> <tr> <th style="vertical-align: top; text-align: left; white-space: normal; border-style: solid solid solid solid; border-width: 0pt 0pt 0.8pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">N</th><td style="vertical-align: top; text-align: right; white-space: normal; border-style: solid solid solid solid; border-width: 0.4pt 0pt 0.8pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">1000       </td></tr> <tr> <th colspan="2" style="vertical-align: top; text-align: left; white-space: normal; border-style: solid solid solid solid; border-width: 0.8pt 0pt 0pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;"> *** p < 0.001; ** p < 0.01; * p < 0.05.</th></tr> </table> --- # Graphically <!-- --> --- # Controlling - We achieve all this just by adding the variable to the OLS equation! - We can, of course, include more than one control, or controls that aren't binary - Use OLS to predict `\(X\)` using all the controls, then take the residual (the part not explained by the controls) - Use OLS to predict `\(Y\)` using all the controls, then take the residual (the part not explained by the controls) - Now do OLS of just the `\(Y\)` residuals on just the `\(X\)` residuals --- # A Continuous Control <img src="data:image/gif;base64,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width="800px" /> --- # What do we get? - We can remove some of the relationship between `\(X\)` and `\(\varepsilon\)` - Potentially all of it, making `\(\hat{\beta}_1\)` us an *unbiased* (i.e. correct on average, but sampling variation doesn't go away!) estimate of `\(\beta_1\)` - Maybe we can also get some estimates of `\(\beta_2\)`, `\(\beta_3\)`... but be careful, they're subject to the same identification and endogeneity problems! - Often in econometrics we focus on getting *one* parameter, `\(\hat{\beta}_1\)`, exactly right and don't focus on parameters we haven't put much effort into identifying --- # Concept Checks - Selene is a huge bore at parties, but sometimes brings her girlfriend Donna who is super fun. If you regressed `\(PartyFunRating\)` on `\(SeleneWasThere\)` but not `\(DonnaWasThere\)`, what would the coefficient on `\(SeleneWasThere\)` look like and why? - Describe the steps necessary to estimate the effect of `\(Exports\)` on `\(GrowthRate\)` while controlling for `\(AmountofConflict\)` (a continuous variable). There are three "explain/regress" steps and two "subtract" steps. - If we estimate the same `\(\hat{\beta}_1\)` with or without `\(Z\)` added as a control, does that mean we have no endogeneity problem? What *does* it mean exactly? --- # Have We Solved It? - Including controls for every part of (what used to be) `\(\varepsilon\)` that is related to `\(X\)` clears up any endogeneity problem we had with `\(X\)` - So... when we add a control, does that do it? How do we know? - Inconveniently, the data alone will never tell us if we've solved endogeniety - We can't just check `\(X\)` against the remaining `\(\varepsilon\)` because we never *see* `\(\varepsilon\)` - what we have left over after a regression is the real-world *residual*, not the true-model *error* --- # Causal Diagrams - "What do I have to control for to solve the endogeneity problem" is an important and difficult question! - To answer it we need to think about the data-generating process - One way to do that is to draw a *causal diagram* - A causal diagram describes the variables responsible for generating data and how they cause each other - Once we have written down our diagram, we'll know what we need to control for - (hopefully we have data on everything we need to control for! Often we don't) --- # Drawing a Diagram - Endogeneity is all about the *alternate reasons why* two variables might be related *other than the causal effect you want - We can represent *all* the reasons two variables are related with a diagram - Put down on paper how you think the world works, and where you think the data came from! This is economic modeling but with less math 1. List out all the variables relevant to the DGP (including the ones we can't measure or put our finger on!) 2. Draw arrows between them reflecting what causes what else 3. List all the paths from `\(X\)` to `\(Y\)` - these paths are reasons why `\(X\)` and `\(Y\)` are related! 4. Control for at least one variable on each path you *want to close* (isn't the effect you want) --- # Drawing a Diagram <!-- --> --- # Drawing a Diagram - We observe that, in the data, `\(ShortsWearing\)` and `\(IceCreamEating\)` are related. Why? - Maybe, we theorize, that wearing shorts causes you to eat ice cream ( `\(ShortsWearing \rightarrow IceCreamEating\)` ) - However, there's another explanation/path: `\(Temperature\)` causes both ( `\(ShortsWearing \leftarrow Temperature \rightarrow IceCreamEating\)` ) - We need to control for temperature to *close this path!* - Once it's closed, the only path left is `\(ShortsWearing \rightarrow IceCreamEating\)`, so if we *do* see a relationship still in the data, we know we've identified the causal effect --- # Detailing Paths - The goal is to list all the paths that go from the *cause* of our choice to the *outcome* variable (no loops) - That way we know what we need to control for to close the paths! - Control for any one variable on the path, and suddenly there's no variation from that variable any more - the causal chain is broken and the path is closed! - A path counts no matter which direction the arrows point on it (the arrow direction matters but we'll get to that next time) --- # Preschool and Adult Earnings Does going to preschool improve your earnings as an adult? <!-- --> --- # Paths 1. `\(Preschool \rightarrow Earnings\)` 2. `\(Preschool \rightarrow Skills \rightarrow Earnings\)` 3. `\(Preschool \leftarrow Location \rightarrow Earnings\)` 4. `\(Preschool \leftarrow Background \rightarrow Earnings\)` 5. `\(Preschool \leftarrow Background \rightarrow Skills \rightarrow Earnings\)` 6. `\(Preschool \rightarrow Skills \leftarrow Background \rightarrow Earnings\)` --- # Closing Paths - We want the ways that `\(Preschool\)` causes `\(Earnings\)` - that's the first two, `\(Preschool \rightarrow Earnings\)` and `\(Preschool \rightarrow Skills \rightarrow Earnings\)` - The rest we want to close! - `\(Location\)` is on #3, so if we control for `\(Location\)`, 3 is closed - `\(Background\)` is on the rest, so if we control for `\(Background\)`, the rest are closed - So if we estimate the below OLS equation, `\(\hat{\beta}_1\)` will be unbiased! `$$Earnings = \beta_0 + \beta_1Preschool + \beta_2Location + \beta_3Background+\varepsilon$$` --- # And the Bad News... - This assumes that *the model we drew was accurate*. Did we leave any important variables or arrows out? Think hard! - What other variables might belong on this graph? Would they be on a path that gives an alternate explanation? - Just because we *say* that's the model doesn't magically make it the *actual model!* It needs to be right! Use that economic theory and common sense to think about missing parts of the graph - Also, *can* we control for those things. What would it mean to assign a single number for `\(Background\)` to someone? Or if we're representing `\(Background\)` with multiple variables - race, gender, parental income, etc., how do we know if we've fully covered it? --- # And the Bad News... - Regardless, this is the kind of thinking we have to do to figure out how to identify things by controlling for variables - There's no way to get around having to make these sorts of assumptions if we want to identify a causal effect - Really! No way at all! Even experiments have assumptions - The key is not avoiding assumptions, but making sure they're reasonable, and verifying those assumptions where you can --- # An Example - Let's back off of those concerns a moment and generate the data ourselves so we know the truth! - In the below data generating process, what is the true effect of `\(X\)` on `\(Y\)`? - Let's figure out how to draw the causal diagram for this data generating process! - (note: `U1`, `U2`, etc., often stand in as an unobserved common cause for two variables that are *correlated* but we think neither causes the other) ```r tib <- tibble(U1 = rnorm(1000), A = rnorm(1000), B = rnorm(1000)) %>% mutate(C = U1 + rnorm(1000), D = U1 + rnorm(1000)) %>% mutate(X = A + C + rnorm(1000)) %>% mutate(Y = 4*X + A + B + D + rnorm(1000)) m1 <- lm(Y~X, data = tib) m1$coefficients ``` ``` ## (Intercept) X ## -0.04049079 4.51062043 ``` --- # The Diagram - Here's the diagram we can draw from that information. What paths are there from `X` to `Y`? <!-- --> --- # The Paths 1. `\(X \rightarrow Y\)` 2. `\(X \leftarrow A \rightarrow Y\)` 3. `\(X \leftarrow C \leftarrow U_1 \rightarrow D \rightarrow Y\)` What do we *need* to control for to close all the paths we don't want? Assume we can't observe (and so can't control for) `\(U_1\)` --- # The Adjusted Analysis - Remember, the true `\(\beta_1\)` was 4 <table class="huxtable" style="border-collapse: collapse; border: 0px; margin-bottom: 2em; margin-top: 2em; ; margin-left: auto; margin-right: auto; " id="tab:unnamed-chunk-14"> <col><col><col><col><tr> <th style="vertical-align: top; text-align: center; white-space: normal; border-style: solid solid solid solid; border-width: 0.8pt 0pt 0pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;"></th><th style="vertical-align: top; text-align: center; white-space: normal; border-style: solid solid solid solid; border-width: 0.8pt 0pt 0.4pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">Model 1</th><th style="vertical-align: top; text-align: center; white-space: normal; border-style: solid solid solid solid; border-width: 0.8pt 0pt 0.4pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">Model 2</th><th style="vertical-align: top; text-align: center; white-space: normal; border-style: solid solid solid solid; border-width: 0.8pt 0pt 0.4pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">Model 3</th></tr> <tr> <th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">(Intercept)</th><td style="vertical-align: top; text-align: right; white-space: normal; border-style: solid solid solid solid; border-width: 0.4pt 0pt 0pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">-0.04    </td><td style="vertical-align: top; text-align: right; white-space: normal; border-style: solid solid solid solid; border-width: 0.4pt 0pt 0pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">-0.03    </td><td style="vertical-align: top; text-align: right; white-space: normal; border-style: solid solid solid solid; border-width: 0.4pt 0pt 0pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">0.02    </td></tr> <tr> <th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;"></th><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">(0.06)   </td><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">(0.06)   </td><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">(0.05)   </td></tr> <tr> <th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">X</th><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">4.51 ***</td><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">4.00 ***</td><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">4.00 ***</td></tr> <tr> <th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;"></th><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">(0.03)   </td><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">(0.06)   </td><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">(0.03)   </td></tr> <tr> <th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">A</th><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">       </td><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">1.04 ***</td><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">0.98 ***</td></tr> <tr> <th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;"></th><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">       </td><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">(0.08)   </td><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">(0.05)   </td></tr> <tr> <th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">C</th><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">       </td><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">0.48 ***</td><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">       </td></tr> <tr> <th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;"></th><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">       </td><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">(0.07)   </td><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">       </td></tr> <tr> <th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">D</th><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">       </td><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">       </td><td style="vertical-align: top; text-align: right; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">0.98 ***</td></tr> <tr> <th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;"></th><td style="vertical-align: top; text-align: right; white-space: normal; border-style: solid solid solid solid; border-width: 0pt 0pt 0.4pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">       </td><td style="vertical-align: top; text-align: right; white-space: normal; border-style: solid solid solid solid; border-width: 0pt 0pt 0.4pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">       </td><td style="vertical-align: top; text-align: right; white-space: normal; border-style: solid solid solid solid; border-width: 0pt 0pt 0.4pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">(0.04)   </td></tr> <tr> <th style="vertical-align: top; text-align: left; white-space: normal; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">N</th><td style="vertical-align: top; text-align: right; white-space: normal; border-style: solid solid solid solid; border-width: 0.4pt 0pt 0pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">1000       </td><td style="vertical-align: top; text-align: right; white-space: normal; border-style: solid solid solid solid; border-width: 0.4pt 0pt 0pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">1000       </td><td style="vertical-align: top; text-align: right; white-space: normal; border-style: solid solid solid solid; border-width: 0.4pt 0pt 0pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">1000       </td></tr> <tr> <th style="vertical-align: top; text-align: left; white-space: normal; border-style: solid solid solid solid; border-width: 0pt 0pt 0.8pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">R2</th><td style="vertical-align: top; text-align: right; white-space: normal; border-style: solid solid solid solid; border-width: 0pt 0pt 0.8pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">0.95    </td><td style="vertical-align: top; text-align: right; white-space: normal; border-style: solid solid solid solid; border-width: 0pt 0pt 0.8pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">0.96    </td><td style="vertical-align: top; text-align: right; white-space: normal; border-style: solid solid solid solid; border-width: 0pt 0pt 0.8pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;">0.98    </td></tr> <tr> <th colspan="4" style="vertical-align: top; text-align: left; white-space: normal; border-style: solid solid solid solid; border-width: 0.8pt 0pt 0pt 0pt; padding: 6pt 6pt 6pt 6pt; font-weight: normal;"> *** p < 0.001; ** p < 0.01; * p < 0.05.</th></tr> </table> --- # Concept Checks - Why did we only need to control for `\(C\)` *or* `\(D\)` in that last example? - Draw a graph with five variables on it: `\(X\)`, `\(Y\)`, `\(A\)`, `\(B\)`, `\(C\)`. Then draw arrows at them completely at random (except to ensure there's no "loop" where you can follow an arrow path from arrow base to head and end up where you started). Then list every path from `\(X\)` to `\(Y\)` and say what you'd need to control for to identify the effect - What would you need to control for to estimate the effect of "drinking a glass of wine a day" on "lifespan"? Draw a diagram.